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Principle of covariance : ウィキペディア英語版
Principle of covariance
In physics, the principle of covariance emphasizes the formulation of physical laws using only certain physical quantities such that their measurements in different frames of reference can be unambiguously correlated (via Lorentz transformations).
Mathematically, the physical quantities must transform ''covariantly'', that is, under a certain representation of the group of coordinate transformations between admissible frames of reference of the physical theory.〔E.J.Post,
''Formal Structure of Electromagnetics: General Covariance and Electromagnetics'', Dover publications〕 This group is referred to as the covariance group.
Principle of covariance does not require invariance of the physical laws under the group of admissible transformations although in most cases the equations are actually invariant. However, in the theory of weak interactions the equations are not invariant under reflections (but are, of course, still covariant).
== Covariance in Newtonian mechanics ==
In Newtonian mechanics the admissible frames of reference are inertial frames with relative velocities much smaller than the speed of light. Time is then absolute and the transformations between admissible frames of references are Galilean transformations which (together with rotations, translations, and reflections) form the Galilean group. The covariant physical quantities are Euclidean scalars, vectors, and tensors. An example of a covariant equation is Newton's second law,
:
m\frac=\vec,

where the covariant quantities are the mass m of a moving body (scalar), the velocity \vec of the body (vector), the force \vec acting on the body, and the invariant time t.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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